Course module

Section 3 | समुच्चय, संबंध, फलन, तर्क एवं ग्राफ / Sets, Relations, Functions, Logic & Graphs — BPSC TRE 4.0 PGT Mathematics (कक्षा 11–12)

विषय भाग (80 प्रश्न): वरिष्ठ माध्यमिक शिक्षक स्तर पर इकाई-वार MCQ अभ्यास। / Unit-wise MCQ practice at PGT depth for the subject section (80 questions). Set Theory / Relations / Functions / Propositional and Predicate Logic / Graph Theory.

Explore the module outline and lessons below. Enroll free to begin studying here.

Return to /learn/BPSC-TRE-4-SENIOR-SECONDARY-TEACHER-CLASS-11-12-MATHEMATICS/subject-discrete after enrolling
Lessons
43
Duration
—
PYQs
6
Practice
49

5% of this course's PYQ weight is covered in this module.

Syllabus index

Lessons in this module

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

  1. Sets, Representation of Sets and Hierarchy of numbersPdf

Finite, Infinite, Countable, and Uncountable Sets

  1. Finite, Infinite, Countable, and Uncountable SetsPdf

Null, Universal, Subsets, Proper Subsets

  1. Null, Universal, Subsets, Proper SubsetsPdf

Power Set and its Cardinality

  1. Power Set and its CardinalityPdf

Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and Complement

  1. Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and ComplementPdf

Relations

Cartesian Product, Relation, Inverse & Complement

  1. Cartesian Product, Relation, Inverse & ComplementPdf

Reflexive Irreflexive Relation – Count, and Properties

  1. Reflexive Irreflexive Relation – Count, and PropertiesPdf

Symmetric Anti-Symmetric Asymmetric Relation and Properties

  1. Symmetric Anti-Symmetric Asymmetric Relation and PropertiesPdf

Transitive Relation – Definition, Count, and Properties

  1. Transitive Relation – Definition, Count, and PropertiesPdf

Equivalence Relation, Equivalence Classes, Partitions of a Set

  1. Equivalence Relation, Equivalence Classes, Partitions of a SetPdf

Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order Relation

  1. Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order RelationPdf

Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower Bound

  1. Hasse Diagram, Greatest Element, Least Element, Upper Bound, Lower BoundPdf

Functions

Definition of a Function – Domain, Co-domain, Range, and Count of Possible Functions

  1. Definition of a Function – Domain, Co-domain, Range, and Count of Possible FunctionsPdf

Composition of Functions – Definition, Properties, and Examples

  1. Composition of Functions – Definition, Properties, and ExamplesPdf

One-to-One (Injective) Function – Definition, Count, and Properties

  1. One-to-One (Injective) Function – Definition, Count, and PropertiesPdf

Onto (Surjective) Function – Definition, Count, and Properties

  1. Onto (Surjective) Function – Definition, Count, and PropertiesPdf

Bijective Function – Definition, Count, and Properties

  1. Bijective Function – Definition, Count, and PropertiesPdf

Inverse of a Function – Definition, Existence Conditions, and Examples

  1. Inverse of a Function – Definition, Existence Conditions, and ExamplesPdf

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

  1. Introduction to Propositions, Laws of Contradiction and Excluded MiddlePdf

Types of Propositions – Atomic and Compound

  1. Types of Propositions – Atomic and CompoundPdf

Logical Operators – Negation, Conjunction, and Disjunction

  1. Logical Operators – Negation, Conjunction, and DisjunctionPdf

Implication and Bi-Conditional Operators in Logic

  1. Logical Operators – Negation, Conjunction, and DisjunctionPdf

Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and Validity

  1. Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and ValidityPdf

Introduction to First Order Predicate Logic

  1. Introduction to First Order Predicate LogicPdf

Quantifiers – Universal and Existential

  1. Quantifiers – Universal and ExistentialPdf

Practice Problems on Quantifiers and Predicate Logic

  1. Practice Problems on Quantifiers and Predicate LogicPdf

Graph Theory

Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)

  1. Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)Pdf

Types of Graphs – Finite, Infinite, Null, Trivial, Complete

  1. Types of Graphs – Finite, Infinite, Null, Trivial, CompletePdf

Bipartite, Cycle, Regular, and Complement of a Graph

  1. Bipartite, Cycle, Regular, and Complement of a GraphPdf

Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree Sequence

  1. Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree SequencePdf

Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi Theorem

  1. Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi TheoremPdf

Graph Traversal – Walk, Path, Trail, Circuit, and Connected Graphs

  1. Graph Traversal – Walk, Path, Trail, Circuit, and Connected GraphsPdf

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

  1. Euler and Hamiltonian Graphs – Definitions, Conditions, and ExamplesPdf

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

  1. Planar Graphs – Kuratowski’s Theorems, Homorphism and examplesPdf

Euler Formula – Planar Graph Formula, Applications, and Derived Relations

  1. Euler Formula – Planar Graph Formula, Applications, and Derived RelationsPdf

Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring Theorems

  1. Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring TheoremsPdf

Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and Center

  1. Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and CenterPdf

Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set Concepts

  1. Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set ConceptsPdf

Previous-year questions

PYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions2 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions2 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions1 questionsPYQ collectionPYQ Questions6 questions

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Previous moduleSection 3 | क्रमचय-संचय, प्रायिकता एवं सांख्यिकी / Combinatorics, Probability & StatisticsNext moduleSection 3 | रैखिक बीजगणित / Linear Algebra
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